Subgroups — C₁₃₇×#19907 #46869293

Order 35072.

602 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3393×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	Q₈×D₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#3328×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#1707×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1699×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1674×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1670×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1652×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1651×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	#1589×C₁₃₇	C₂	1	1	yes	maximal, characteristic
11	C₈×Q₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#556×C₁₃₇	C₂²	1	2	yes	—
13	D₄×Q₈×C₁₃₇	C₂²	1	2	yes	—
14	#500×C₁₃₇	—	2	1	no	—
15	#500×C₁₃₇	C₂²	1	1	yes	characteristic
16	#498×C₁₃₇	C₂²	1	2	yes	—
17	#495×C₁₃₇	—	2	1	no	—
18	#494×C₁₃₇	C₂²	1	1	yes	characteristic
19	#487×C₁₃₇	C₂²	1	2	yes	—
20	#485×C₁₃₇	—	2	2	no	—
21	#475×C₁₃₇	C₂²	1	2	yes	—
22	#474×C₁₃₇	—	2	2	no	—
23	#474×C₁₃₇	C₂²	1	2	yes	—
24	#470×C₁₃₇	—	2	2	no	—
25	#464×C₁₃₇	—	2	2	no	—
26	#462×C₁₃₇	C₂²	1	2	yes	—
27	#461×C₁₃₇	C₂²	1	2	yes	—
28	#451×C₁₃₇	—	2	2	no	—
29	C₈×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
30	C₈×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
31	C₄×Q₁₆×C₁₃₇	—	2	1	no	—
32	C₄×Q₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
33	C₄×D₈×C₁₃₇	—	2	1	no	—
34	C₄×D₈×C₁₃₇	C₂²	1	1	yes	characteristic
35	#436×C₁₃₇	C₂²	1	2	yes	—
36	#419×C₁₃₇	—	2	2	no	—
37	#335×C₁₃₇	C₂²	1	1	yes	characteristic
38	#335×C₁₃₇	C₂²	1	1	yes	characteristic
39	#332×C₁₃₇	C₂²	1	2	yes	—
40	#332×C₁₃₇	C₂²	1	2	yes	—
41	Q₈⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
42	Q₈⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
43	D₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
44	C₈²×C₁₃₇	C₂²	1	1	yes	characteristic
45	C₂²×Q₈×C₁₃₇	—	2	2	no	—
46	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
47	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
48	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
49	C₂×Q₁₆×C₁₃₇	D₄	1	1	yes	characteristic
50	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
51	C₂×D₈×C₁₃₇	D₄	1	1	yes	characteristic
52	C₂×M₁₆×C₁₃₇	—	2	2	no	—
53	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
54	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
55	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
56	#126×C₁₃₇	—	4	2	no	—
57	#124×C₁₃₇	—	2	2	no	—
58	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
59	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
60	C₂²⋊Q₈×C₁₃₇	—	4	2	no	—
61	C₄×Q₈×C₁₃₇	—	2	2	no	—
62	C₄×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
63	C₄×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
64	C₄×D₄×C₁₃₇	—	2	2	no	—
65	C₄×D₄×C₁₃₇	C₂³	1	2	yes	—
66	#117×C₁₃₇	—	2	2	no	—
67	#107×C₁₃₇	—	2	1	no	—
68	#107×C₁₃₇	—	2	1	no	—
69	#107×C₁₃₇	—	2	2	no	—
70	#107×C₁₃₇	D₄	1	1	yes	characteristic
71	#107×C₁₃₇	D₄	1	1	yes	characteristic
72	#106×C₁₃₇	—	2	2	no	—
73	#106×C₁₃₇	—	4	2	no	—
74	C₄⋊C₈×C₁₃₇	—	2	1	no	—
75	C₄⋊C₈×C₁₃₇	—	2	1	no	—
76	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
77	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
79	#103×C₁₃₇	—	2	2	no	—
80	#103×C₁₃₇	—	2	2	no	—
81	#103×C₁₃₇	—	2	2	no	—
82	#103×C₁₃₇	—	2	2	no	—
83	#103×C₁₃₇	—	2	2	no	—
84	#103×C₁₃₇	D₄	1	1	yes	characteristic
85	#103×C₁₃₇	D₄	1	1	yes	characteristic
86	#102×C₁₃₇	—	2	2	no	—
87	#102×C₁₃₇	D₄	1	2	yes	—
88	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
89	C₄×C₈×C₁₃₇	—	2	1	no	—
90	C₄×C₈×C₁₃₇	—	2	1	no	—
91	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₁₃₇	—	2	2	no	—
95	C₂×Q₈×C₁₃₇	—	2	2	no	—
96	C₂×Q₈×C₁₃₇	—	4	2	no	—
97	C₂×Q₈×C₁₃₇	—	4	4	no	—
98	C₂×Q₈×C₁₃₇	—	8	2	no	—
99	C₂×Q₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
100	C₂×Q₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
101	C₂×D₄×C₁₃₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₃₇	—	2	2	no	—
103	C₂²×C₄×C₁₃₇	—	4	2	no	—
104	Q₁₆×C₁₃₇	—	2	2	no	—
105	Q₁₆×C₁₃₇	—	4	2	no	—
106	Q₁₆×C₁₃₇	—	8	1	no	—
107	Q₁₆×C₁₃₇	—	8	2	no	—
108	SD₁₆×C₁₃₇	—	8	2	no	—
109	D₈×C₁₃₇	—	2	2	no	—
110	M₁₆×C₁₃₇	—	8	2	no	—
111	C₂×C₈×C₁₃₇	—	2	1	no	—
112	C₂×C₈×C₁₃₇	—	2	1	no	—
113	C₂×C₈×C₁₃₇	—	2	1	no	—
114	C₂×C₈×C₁₃₇	—	2	2	no	—
115	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
119	C₄⋊C₄×C₁₃₇	—	2	1	no	—
120	C₄⋊C₄×C₁₃₇	—	2	1	no	—
121	C₄⋊C₄×C₁₃₇	—	2	2	no	—
122	C₄⋊C₄×C₁₃₇	—	2	2	no	—
123	C₄⋊C₄×C₁₃₇	—	2	2	no	—
124	C₄⋊C₄×C₁₃₇	—	2	2	no	—
125	C₄⋊C₄×C₁₃₇	—	4	2	no	—
126	C₄⋊C₄×C₁₃₇	—	4	2	no	—
127	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
129	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
130	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
131	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
132	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
133	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
134	C₄²×C₁₃₇	—	2	1	no	—
135	C₄²×C₁₃₇	—	2	1	no	—
136	C₄²×C₁₃₇	—	4	2	no	—
137	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
138	C₂³×C₁₃₇	—	2	2	no	—
139	Q₈×C₁₃₇	—	2	1	no	—
140	Q₈×C₁₃₇	—	2	1	no	—
141	Q₈×C₁₃₇	—	2	1	no	—
142	Q₈×C₁₃₇	—	4	2	no	—
143	Q₈×C₁₃₇	—	4	2	no	—
144	Q₈×C₁₃₇	—	4	2	no	—
145	Q₈×C₁₃₇	—	4	2	no	—
146	Q₈×C₁₃₇	—	8	4	no	—
147	Q₈×C₁₃₇	#135	1	2	yes	—
148	D₄×C₁₃₇	—	2	2	no	—
149	D₄×C₁₃₇	—	2	2	no	—
150	C₂×C₄×C₁₃₇	—	2	1	no	—
151	C₂×C₄×C₁₃₇	—	2	1	no	—
152	C₂×C₄×C₁₃₇	—	2	1	no	—
153	C₂×C₄×C₁₃₇	—	2	1	no	—
154	C₂×C₄×C₁₃₇	—	2	2	no	—
155	C₂×C₄×C₁₃₇	—	4	2	no	—
156	C₂×C₄×C₁₃₇	—	4	2	no	—
157	C₂×C₄×C₁₃₇	—	4	2	no	—
158	C₂×C₄×C₁₃₇	—	4	2	no	—
159	C₂×C₄×C₁₃₇	—	8	4	no	—
160	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
163	C₈×C₁₃₇	—	2	2	no	—
164	C₈×C₁₃₇	—	2	1	no	—
165	C₈×C₁₃₇	—	2	1	no	—
166	C₈×C₁₃₇	—	2	1	no	—
167	C₈×C₁₃₇	—	4	2	no	—
168	C₈×C₁₃₇	—	4	1	no	—
169	C₈×C₁₃₇	—	4	1	no	—
170	C₈×C₁₃₇	#137	1	2	yes	—
171	C₂²×C₁₃₇	—	4	2	no	—
172	C₂²×C₁₃₇	—	4	2	no	—
173	C₂²×C₁₃₇	—	4	2	no	—
174	C₂²×C₁₃₇	D₄²	1	1	yes	characteristic
175	C₄×C₁₃₇	—	2	2	no	—
176	C₄×C₁₃₇	—	2	1	no	—
177	C₄×C₁₃₇	—	4	2	no	—
178	C₄×C₁₃₇	—	4	1	no	—
179	C₄×C₁₃₇	—	4	1	no	—
180	C₄×C₁₃₇	—	4	1	no	—
181	C₄×C₁₃₇	—	8	2	no	—
182	C₄×C₁₃₇	—	8	2	no	—
183	C₄×C₁₃₇	C₂×#135	1	1	yes	characteristic
184	C₄×C₁₃₇	C₂×#137	1	1	yes	characteristic
185	C₄×C₁₃₇	#576	1	1	yes	characteristic
186	C₄×C₁₃₇	#577	1	1	yes	characteristic
187	C₂×C₁₃₇	—	8	2	no	—
188	C₂×C₁₃₇	#3278	1	1	yes	characteristic
189	C₂×C₁₃₇	#3280	1	1	yes	characteristic
190	C₂×C₁₃₇	#3293	1	1	yes	characteristic
191	#19907	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₁₃₇	#19907	1	1	yes	characteristic, direct product factor, Sylow
193	#3393	C₂×C₁₃₇	1	1	yes	characteristic
194	Q₈×D₈	C₂×C₁₃₇	1	1	yes	characteristic
195	#3328	C₂×C₁₃₇	1	2	yes	complemented
196	#1707	C₂×C₁₃₇	1	1	yes	characteristic, complemented
197	#1699	C₂×C₁₃₇	1	2	yes	complemented
198	#1674	C₂×C₁₃₇	1	1	yes	characteristic, complemented
199	#1670	C₂×C₁₃₇	1	1	yes	characteristic, complemented
200	#1652	C₂×C₁₃₇	1	2	yes	complemented
201	#1651	C₂×C₁₃₇	1	2	yes	complemented
202	#1589	C₂×C₁₃₇	1	1	yes	characteristic
203	C₈×Q₁₆	C₂×C₁₃₇	1	1	yes	characteristic, complemented
204	#556	C₂²×C₁₃₇	1	2	yes	—
205	D₄×Q₈	C₂²×C₁₃₇	1	2	yes	—
206	#500	—	2	1	no	—
207	#500	C₂²×C₁₃₇	1	1	yes	characteristic
208	#498	C₂²×C₁₃₇	1	2	yes	—
209	#495	—	2	1	no	—
210	#494	C₂²×C₁₃₇	1	1	yes	characteristic
211	#487	C₂²×C₁₃₇	1	2	yes	—
212	#485	—	2	2	no	—
213	#475	C₂²×C₁₃₇	1	2	yes	—
214	#474	—	2	2	no	—
215	#474	C₂²×C₁₃₇	1	2	yes	—
216	#470	—	2	2	no	—
217	#464	—	2	2	no	—
218	#462	C₂²×C₁₃₇	1	2	yes	—
219	#461	C₂²×C₁₃₇	1	2	yes	—
220	#451	—	2	2	no	—
221	C₈×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
222	C₈×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
223	C₄×Q₁₆	—	2	1	no	—
224	C₄×Q₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
225	C₄×D₈	—	2	1	no	—
226	C₄×D₈	C₂²×C₁₃₇	1	1	yes	characteristic
227	#436	C₂²×C₁₃₇	1	2	yes	—
228	#419	—	2	2	no	—
229	#335	C₂²×C₁₃₇	1	1	yes	characteristic
230	#335	C₂²×C₁₃₇	1	1	yes	characteristic
231	#332	C₂²×C₁₃₇	1	2	yes	—
232	#332	C₂²×C₁₃₇	1	2	yes	—
233	Q₈⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
234	Q₈⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
235	D₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
236	C₈²	C₂²×C₁₃₇	1	1	yes	characteristic
237	C₂²×Q₈	—	2	2	no	—
238	C₂×Q₁₆	—	2	2	no	—
239	C₂×Q₁₆	—	2	1	no	—
240	C₂×Q₁₆	—	2	1	no	—
241	C₂×Q₁₆	D₄×C₁₃₇	1	1	yes	characteristic
242	C₂×SD₁₆	—	2	2	no	—
243	C₂×D₈	D₄×C₁₃₇	1	1	yes	characteristic
244	C₂×M₁₆	—	2	2	no	—
245	C₄⋊Q₈	—	2	2	no	—
246	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
247	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
248	#126	—	4	2	no	—
249	#124	—	2	2	no	—
250	C₂²⋊Q₈	—	2	2	no	—
251	C₂²⋊Q₈	—	2	2	no	—
252	C₂²⋊Q₈	—	4	2	no	—
253	C₄×Q₈	—	2	2	no	—
254	C₄×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
255	C₄×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
256	C₄×D₄	—	2	2	no	—
257	C₄×D₄	C₂³×C₁₃₇	1	2	yes	—
258	#117	—	2	2	no	—
259	#107	—	2	1	no	—
260	#107	—	2	1	no	—
261	#107	—	2	2	no	—
262	#107	D₄×C₁₃₇	1	1	yes	characteristic
263	#107	D₄×C₁₃₇	1	1	yes	characteristic
264	#106	—	2	2	no	—
265	#106	—	4	2	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
269	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
270	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
271	#103	—	2	2	no	—
272	#103	—	2	2	no	—
273	#103	—	2	2	no	—
274	#103	—	2	2	no	—
275	#103	—	2	2	no	—
276	#103	D₄×C₁₃₇	1	1	yes	characteristic
277	#103	D₄×C₁₃₇	1	1	yes	characteristic
278	#102	—	2	2	no	—
279	#102	D₄×C₁₃₇	1	2	yes	—
280	C₂²⋊C₈	—	2	2	no	—
281	C₄×C₈	—	2	1	no	—
282	C₄×C₈	—	2	1	no	—
283	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
285	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	2	no	—
289	C₂×Q₈	—	4	4	no	—
290	C₂×Q₈	—	8	2	no	—
291	C₂×Q₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
292	C₂×Q₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
293	C₂×D₄	C₂×D₄×C₁₃₇	1	2	yes	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	Q₁₆	—	2	2	no	—
297	Q₁₆	—	4	2	no	—
298	Q₁₆	—	8	1	no	—
299	Q₁₆	—	8	2	no	—
300	SD₁₆	—	8	2	no	—
301	D₈	—	2	2	no	—
302	M₁₆	—	8	2	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
308	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
309	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
310	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
320	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
321	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	4	2	no	—
329	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
330	C₂³	—	2	2	no	—
331	Q₈	—	2	1	no	—
332	Q₈	—	2	1	no	—
333	Q₈	—	2	1	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	4	2	no	—
336	Q₈	—	4	2	no	—
337	Q₈	—	4	2	no	—
338	Q₈	—	8	4	no	—
339	Q₈	#135×C₁₃₇	1	2	yes	—
340	D₄	—	2	2	no	—
341	D₄	—	2	2	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	8	4	no	—
352	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
353	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
354	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
355	C₈	—	2	2	no	—
356	C₈	—	2	1	no	—
357	C₈	—	2	1	no	—
358	C₈	—	2	1	no	—
359	C₈	—	4	2	no	—
360	C₈	—	4	1	no	—
361	C₈	—	4	1	no	—
362	C₈	#137×C₁₃₇	1	2	yes	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	4	2	no	—
366	C₂²	D₄²×C₁₃₇	1	1	yes	characteristic
367	C₄	—	2	1	no	—
368	C₄	—	2	2	no	—
369	C₄	—	4	1	no	—
370	C₄	—	4	1	no	—
371	C₄	—	4	2	no	—
372	C₄	—	4	1	no	—
373	C₄	—	8	2	no	—
374	C₄	—	8	2	no	—
375	C₄	C₂×#135×C₁₃₇	1	1	yes	characteristic
376	C₄	C₂×#137×C₁₃₇	1	1	yes	characteristic
377	C₄	#576×C₁₃₇	1	1	yes	characteristic
378	C₄	#577×C₁₃₇	1	1	yes	characteristic
379	C₂	—	8	2	no	—
380	C₂	#3278×C₁₃₇	1	1	yes	characteristic
381	C₂	#3280×C₁₃₇	1	1	yes	characteristic
382	C₂	#3293×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
prime radical	C₂×D₈×C₁₃₇	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₄²×C₁₃₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. #3328×C₁₃₇	C₂	semidirect
4. #1707×C₁₃₇	C₂	semidirect
5. #1699×C₁₃₇	C₂	semidirect
6. #1674×C₁₃₇	C₂	semidirect
7. #1670×C₁₃₇	C₂	semidirect
8. #1652×C₁₃₇	C₂	semidirect
9. #1651×C₁₃₇	C₂	semidirect
11. C₈×Q₁₆×C₁₃₇	C₂	semidirect
191. #19907	C₁₃₇	direct (N × H)
192. C₁₃₇	#19907	direct (N × H)
195. #3328	C₂×C₁₃₇	semidirect
196. #1707	C₂×C₁₃₇	semidirect
197. #1699	C₂×C₁₃₇	semidirect
198. #1674	C₂×C₁₃₇	semidirect
199. #1670	C₂×C₁₃₇	semidirect
200. #1652	C₂×C₁₃₇	semidirect
201. #1651	C₂×C₁₃₇	semidirect
203. C₈×Q₁₆	C₂×C₁₃₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#3393×C₁₃₇	2
Q₈×D₈×C₁₃₇	2
#3328×C₁₃₇	2
#1707×C₁₃₇	2
#1699×C₁₃₇	2
#1674×C₁₃₇	2
#1670×C₁₃₇	2
#1652×C₁₃₇	2
#1651×C₁₃₇	2
#1589×C₁₃₇	2
C₈×Q₁₆×C₁₃₇	2
#19907	137

Subgroups — C137×#19907 #46869293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#19907 #46869293